This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A035670 #17 Jan 03 2025 09:28:02
%S A035670 0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,2,1,0,1,2,2,2,4,2,2,2,6,4,6,6,6,4,8,
%T A035670 10,10,10,13,11,12,14,21,18,21,21,25,22,30,34,37,35,41,42,46,50,63,61,
%U A035670 66,67,79,78,93,100,110,107,120,128,141,149,172,175,186,192,220,226
%N A035670 Number of partitions of n into parts 7k+4 and 7k+6 with at least one part of each type.
%H A035670 Robert Price, <a href="/A035670/b035670.txt">Table of n, a(n) for n = 1..1000</a>
%F A035670 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7*k + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(7*k + 6))). - _Robert Price_, Aug 15 2020
%t A035670 nmax = 75; s1 = Range[0, nmax/7]*7 + 4; s2 = Range[0, nmax/7]*7 + 6;
%t A035670 Table[Count[IntegerPartitions[n, All, s1~Join~s2], x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035670 nmax = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 4)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020 *)
%Y A035670 Cf. A035441-A035468, A035618-A035669, A035671-A035699.
%K A035670 nonn
%O A035670 1,17
%A A035670 _Olivier Gérard_